As the simplest molecules with only one electron and two nuclei in nature, H2+ and its isotopes are of special importance and serve as benchmark systems for ultrafast science and technologies. Their dissociation in strong laser fields has attracted a lot of interests in past decades because it directly relates to the production of chemical reactions, and a series of great achievements have already been made successively under the cooperative efforts between the theoretical and experimental physicists. With the rapid technological development of lasers as well as the advanced experimental techniques in recent years, some new trends in this topic are presented. In this paper, we focus on recent research progress of experimental and theoretical works on hydrogen molecular ions dissociation. We first give a background information about past achievements, and then introduce general numerical methods to deal with dissociation, i.e., the numerical simulation of the time-dependent Schrodinger equation (TDSE), and the combination of the strong field approximation and TDSE simulation. The latter was developed to investigate dissociative ionization of hydrogen molecules. Next three related hot research topics are reviewed sequentially, including interference between dissociation channels, photon energy sharing between electron and nuclei, and molecular rotation in dissociation. In detail, some strategies have been raised to control the unique electron localization after the molecular dissociation, which is due to the interference between the lowest two electronic states with opposite parities. In addition, the pump-probe technique was also utilized to observe electron localization dynamics in real time. However, interference of nuclear wave packets carrying different angular momenta in the same electronic state and ending with the same momentum contributes novel spiral momentum distribution under a circularly polarized laser pulse. The electron-nuclear correlation for different ionization mechanisms is mainly indicated in the joint energy spectra, which was extracted and explained by coincident measurement and various theoretical methods. The molecular rotation is generally assumed frozen in dissociation process, which is the common axial recoil approximation. However, recent theoretical and experimental researches show that the ultrafast electron dynamics may play roles in the molecular rotation though their timescales are significantly different. In conclusion, the studies of hydrogen molecular ions not only further deepen our understanding of ultrafast dynamics in small molecules, but also shed light on observing, understanding, and ultimately controlling complex chemical reactions.
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